Question

In how many ways 6 rings of different types can be worn in 4 fingers?

Answer 1

Hint: We will first start by finding the way in which one ring can be worn in 4 fingers. Then we will do the same for 6 rings and then using the fundamental principle of counting we will find the total ways.

Complete step-by-step answer:
Now, we have been given that there are 6 rings of different types and we have to find the ways in which they can be worn in 4 fingers.
Now, we know that the number of options each ring has is 4, that is each ring has 4 fingers as their possible way as it can be worn in any one of 4 fingers.
Now, similarly the other rings will have four options as it has not been mentioned in the options that there has to be at least a ring in a finger. So, each ring has four options i.e. four fingers.
Now, we know that by the fundamental principle of counting there can be \[4\times 4\times 4\times 4\times 4\times 4\] ways of wearing 6 rings.
So, we have ${{4}^{6}}=4096$ ways to wear 6 different types of rings.

Note: It is important to note that we have used a basic fundamental principle of counting to find the total ways. Also, it is important to notice that each ring has 4 ways as it has not been given that each finger must have at least one ring. So, there can be 6 rings in a finger alone and remaining all the fingers empty.